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Superization and \((q,t)\)-specialization in combinatorial Hopf algebras. (English) Zbl 1230.05281
Summary: We extend a classical construction on symmetric functions, the superization process, to several combinatorial Hopf algebras, and obtain analogs of the hook-content formula for the \((q, t)\)-specializations of various bases. Exploiting the dendriform structures yields in particular \((q, t)\)-analogs of the Björner-Wachs \(q\)-hook-length formulas for binary trees, and similar formulas for plane trees.

MSC:
05E05 Symmetric functions and generalizations
05C05 Trees
16T30 Connections of Hopf algebras with combinatorics
18D50 Operads (MSC2010)
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